Finite Elements Simulation of Mechanical Behaviour of Shape Memory Alloys Coupled with a Non-Stationary Thermal Field

Abstract

Abstract. The main deformation mechanisms of shape memory alloys (SMA) are related to martensitic transformation and/or martensitic rwrientation. These phenomena lead to heat production resulting from the transformation andlor from internal dissipation processes. As the SMA behaviour is strongly temperature dependent, its modelling has to take into account thennomechanical coupling. A 3-dimensional finite element code has been designed for that purpose. The quasi-static mechanical behaviour is described through the temperature dependent elastohysteresis model. Large displacements and large deformations are considered. The numerical problem is strongly non-linear and an implicit resolution scheme has been adopted. Two coupled thennomechanical calculations are presented. The first one deals with the one-way memory effect of a cantilever beam. The second one simulates the non-stationary thermal and mechanical fields of this beam during a near-adiabatic pseudoelastic bending.

Roundrobin SMA modeling

“…However, few models adopt the decomposition of the stress tensor in a reversible part and a hysteretic one [29]. The reversible stress is derived from a hyperelastic theory by assuming an expression of the density energy.…”

“…The macroscopic models are derived from thermodynamical approach, [20,[22][23][24][25]27,31] or plasticity and viscoplasticity theories, [21,26,[28][29][30][32][33]. In the first case, a thermodynamical potential expression is assumed or derived from micromechanical considerations.…”

“…SMA models applicable for simulation of adaptive structures with SMA elements can be roughly divided between microscopic models (internal variables are defined at the grain scale, [14][15][16][17][18][19]) and macroscopic models (internal variables are defined at the representative volume element /RVE/, [20][21][22][23][24][25][26][27][28][29][30][31][32][33]). …”

Formulation of a thin shell finite element with continuity C0 and convected material frame notion

“…These last two laws have been completed to model mechanical behaviour of shape memory alloy by an elastohysteresis model. For instance, from the calculation of the thermomechanical coupling, a thermomechanical cycling of a Niti shape memory alloys tube for pipe connection has been performed [27]. Moreover, in order to take into account composite material behaviour in large transformations, an orthotropic constitutive law has been developed [23].…”

“…As well as this shell kinematic, HEREZH contains general 3D and beam kinematics [11]. Historically, HEREZH took shape from the desire to develop a software program including thermomechanical behaviour of shape memory alloys [22,28]. Classic linear elasticity Hooke's law, an hyperelastic law laid down to describe large elastic transformations and a pure hysteresis law have been implanted.…”